We have used the detected transitions of HC\(_3\) N and its rare \(^{13}\) C isotopologues observed towards L1157-B1 to estimate the elemental abundance ratio \(^{12}\) C/\(^{13}\) C in the L1157 star-forming region. The transitions of the rare isotopologues \(J\) =10–9, \(J\) =11–10, \(J\) =12–11 of H\(^{13}\) CCCN, HC\(^{13}\) CCN and HCC\(^{13}\) CN were presented in [1]}. The transitions of same quantum numbers of the different \(^{13}\) C isotopologues are very close in frequency, separated by a few GHz at most. These different transitions were observed simultaneously in the ASAI survey, with the advantage of minimizing the calibration uncertainty, which is then dominated by the rms noise of the spectrum.
[1]} showed that the emission of all the HC\(_3\) N isotopologues detected in the millimeter range is optically thin. Hence, the line flux ratio of the \(^{12}\) C to the sum of the \(^{13}\) C isotopologues is equal to three times the elemental abundance ratio \(^{12}\) C/\(^{13}\) C. For the \(J\) =10–9 and
\(J\) =12–11 transitions, we found \(^{12}\) C/\(^{13}\) C= \(66\pm 6\) . For the \(J\) =11-10, we discarded the H\(^{13}\) CCCN line whose intensity is almost twice as bright as the lines of HC\(^{13}\) CCN and HCC\(^{13}\) CN, a dissymmetry which is observed only in this transition and not in the \(J\) =10–9 and
\(J\) =12–11. It then comes \(^{12}\) C/\(^{13}\) C= \(70\pm 10\) , in agreement with the determinations from the \(J\) =10–9 and
\(J\) =12–11.
This direct observational determination of the \(^{12}\) C/\(^{13}\) C ratio in the L1157 star forming region is actually very close to the elemental abundance ratio in the local ISM, equal to 68, [3]}, [4]} and the value assumed in our previous works (see Sect.  2).
